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3 years ago

5

Betty Baker is making her famous chocolate-chocolate chip cake. She uses 2/3 cup of sugar to make a 1/4 sheet cake. How much sug

ar would she need to make a full sheet cake?

1 answer:

Vera_Pavlovna [14]3 years ago

3 0

Answer: 3 1/3

Step-by-step explanation:

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AJKL and ALMN are shown.

seropon [69]

Answer:

mLNM=63

Step-by-step explanation:

triangle JKL is isocelese so mKJL and KLJ are the same

180-72=108

108/2=54

so both mKLJ and mMLN are equal

and since triangle LMN is an isoceles then mLNM and mLMN are equal to each other

so 180-54=126

126/2=63

mLNM=63

7 0

2 years ago

A garden store bought a fountain at a cost of $995.66 and marked it up 100%. Later on, the store marked it down 25%. What was th

Naya [18.7K]

Answer:

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

A furniture designer builds a trapezoidal desk with a semicircular cutout. What is the area of the desk?

nirvana33 [79]

Answer:

$Area = 26478cm^2$

Step-by-step explanation:

Given

See attachment for desk

Required

The area

First, calculate the area of the semicircular cutout

$Area = \frac{\pi r^2}{2}$

Where

$r = 60cm$

So:

$A_1 = \frac{3.14 * 60^2}{2}$

$A_1 = \frac{11304}{2}$

$A_1 = 5652cm^2$

Next, the area of the complete trapezium

$Area= \frac{1}{2}(a + b) * h$

Where

$a = 300$

$b = 2 * r = 2 * 60 = 120$

$h = 153$

So:

$A_2 = \frac{1}{2} * (300 + 120) * 153$

$A_2 = \frac{1}{2} * 420 * 153$

$A_2 = 32130cm^2$

The area of the desk is:

$Area = A_2 - A_1$

$Area = 32130cm^2 - 5652cm^2$

$Area = 26478cm^2$

8 0

3 years ago

Write an expression for the model. Find the sum. options: a) 2 + (–3); 1 b) –3 + 2; 5 c) 2 + 3; 5 d) 2 + (–3); –1

Dima020 [189]

Answer:

c) 2 + 3 = 5 TRUE

d) 2 + (–3) = -1 True

Step-by-step explanation:

When adding integers (positive and negative whole numbers), there are three cases:

Positive and positive increases and sum is positive. Ex. 4 + 6 = 10
Positive and negative where you subtract and take the sign of the larger number. Ex. 3 + -8 = -5 or -3 + 8 = 5
Negative and negative decrease and the sum if negative. Ex. -4 + -6 = -10.

Use these rules to simplify each expression.

a) 2 + (–3) = -1 not 1 FALSE

b) –3 + 2 = -1 not 5 FALSE

c) 2 + 3 = 5 TRUE

d) 2 + (–3) = -1 True

5 0

3 years ago

9. A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

SSSSS [86.1K]

Answer:

Part 4) $r=84\ units$

Part 9) $sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) $sin(\theta)=-\frac{9\sqrt{202}}{202}$

Step-by-step explanation:

Part 4) A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

we know that

The circumference of a circle subtends a central angle of 360 degrees

The circumference is equal to

$C=2\pi r$

using proportion

$\frac{2\pi r}{360^o}=\frac{56\pi}{120^o}$

simplify

$\frac{r}{180^o}=\frac{56}{120^o}$

solve for r

$r=\frac{56}{120^o}(180^o)$

$r=84\ units$

Part 9) Given cos(∅)=-2/3 and ∅ lies in Quadrant III. Find the exact value of sin(∅) in simplified form

Remember the trigonometric identity

$cos^2(\theta)+sin^2(\theta)=1$

we have

$cos(\theta)=-\frac{2}{3}$

substitute the given value

$(-\frac{2}{3})^2+sin^2(\theta)=1$

$\frac{4}{9}+sin^2(\theta)=1$

$sin^2(\theta)=1-\frac{4}{9}$

$sin^2(\theta)=\frac{5}{9}$

square root both sides

$sin(\theta)=\pm\frac{\sqrt{5}}{3}$

we know that

If ∅ lies in Quadrant III

then

The value of sin(∅) is negative

$sin(\theta)=-\frac{\sqrt{5}}{3}$

Part 10) The terminal side of ∅ passes through the point (11,-9). What is the exact value of sin(∅) in simplified form?

see the attached figure to better understand the problem

In the right triangle ABC of the figure

$sin(\theta)=\frac{BC}{AC}$

Find the length side AC applying the Pythagorean Theorem

$AC^2=AB^2+BC^2$

substitute the given values

$AC^2=11^2+9^2$

$AC^2=202$

$AC=\sqrt{202}\ units$

so

$sin(\theta)=\frac{9}{\sqrt{202}}$

simplify

$sin(\theta)=\frac{9\sqrt{202}}{202}$

Remember that

The point (11,-9) lies in Quadrant IV

then

The value of sin(∅) is negative

therefore

$sin(\theta)=-\frac{9\sqrt{202}}{202}$

5 0

3 years ago